DLMF:9.6.E9 (Q2789)

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DLMF:9.6.E9
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    Bi ′ ⁡ ( - z ) = ( z / 3 ) ⁢ ( J - 2 / 3 ⁡ ( ζ ) + J 2 / 3 ⁡ ( ζ ) ) = 1 2 ⁢ ( z / 3 ) ⁢ ( e π ⁢ i / 3 ⁢ H 2 / 3 ( 1 ) ⁡ ( ζ ) + e - π ⁢ i / 3 ⁢ H 2 / 3 ( 2 ) ⁡ ( ζ ) ) = 1 2 ⁢ ( z / 3 ) ⁢ ( e - π ⁢ i / 3 ⁢ H - 2 / 3 ( 1 ) ⁡ ( ζ ) + e π ⁢ i / 3 ⁢ H - 2 / 3 ( 2 ) ⁡ ( ζ ) ) . diffop Airy-Bi 1 𝑧 𝑧 3 Bessel-J 2 3 𝜁 Bessel-J 2 3 𝜁 1 2 𝑧 3 superscript 𝑒 𝜋 𝑖 3 Hankel-H-1-Bessel-third-kind 2 3 𝜁 superscript 𝑒 𝜋 𝑖 3 Hankel-H-2-Bessel-third-kind 2 3 𝜁 1 2 𝑧 3 superscript 𝑒 𝜋 𝑖 3 Hankel-H-1-Bessel-third-kind 2 3 𝜁 superscript 𝑒 𝜋 𝑖 3 Hankel-H-2-Bessel-third-kind 2 3 𝜁 {\displaystyle{\displaystyle\mathrm{Bi}'\left(-z\right)=(z/\sqrt{3})\left(J_{-% 2/3}\left(\zeta\right)+J_{2/3}\left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3% })\left(e^{\pi i/3}{H^{(1)}_{2/3}}\left(\zeta\right)+e^{-\pi i/3}{H^{(2)}_{2/3% }}\left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/3}{H^{(1)}% _{-2/3}}\left(\zeta\right)+e^{\pi i/3}{H^{(2)}_{-2/3}}\left(\zeta\right)\right% ).}}
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    DLMF:9.6.E9
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